Arithmatical - Boat’s and Streams
DIRECTIONS : Problems based on Boats and Streams.
14. |
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? |
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A. 2.4 km |
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B. 2.5 km |
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C. 3 km |
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D. 3.6 km |
Solution |
Speed downstream = (5 + 1) kmph | = 6kmph. |
Speed upstream = (5 -1) kmph | = 4 kmph. |
Let the required distance be x km. |
Then, x/6 + x/4 = 1 |
= 2x + 3x = 12 |
‹=›5x = 12 |
‹=›x = 2.4. |
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15. |
The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is |
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A. 1.2 km |
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B. 1.8 km |
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C. 2.4 km |
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D. 3.6 km |
Solution |
Speed downstreams | =(15 + 3)kmph |
= 18 kmph. |
Distance travelled | (18 x 12/60)km |
= 3.6km. |
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16. |
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is |
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A. 2 mph |
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B. 2.5 mph |
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C. 3 mph |
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D. 4 mph |
Solution |
Speed downstreams | =(10 + x)mph. |
Speed upstreams | =(10 - x)mph. |
= 18 kmph. |
36/(10-x) - 36/(10+x) | = 90/60 |
= 72x ×60 |
= 90(100 - x²) |
x²+48x+100= 0. |
x= 2mph. |
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